On fractional Orlicz-Sobolev spaces

We will survey some recent results on the theory of fractional Orlicz-Sobolev spaces with a special focus on their role in Sobolev type embeddings with an optimal Orlicz target. We will also mention related Hardy type inequalities, criteria for compact embeddings, and limits of these spaces when the smoothness parameter tends to either of its natural endpoints. This is a joint work with Angela Alberico (Napoli), Andrea Cianchi (Firenze) and Lenka Slavíková (Praha).